Merging objects with flush faces, using Boolean union modifier?
I am new in Blender and I was facing the same problem a few days ago, so here is what I did:
One way that solved the &quot;intersection's anomaly&quot; was the Bool Tool addon. After you add this, you can use the shortcut Shift + Ctrl + B  and the Bool Tool options will pop up.
The Bool Tool did not create any issue for me after the union.
Using the Boolean Modifier:
When the union is done, even though you get the anomaly, apply the modifier. Then, in your Collection list you can see that the mesh you tried to merge to your other mesh, is still there. Delete that mesh. The Boolean modifier managed to merge the two meshes, but the mesh that was merged still exists as an individual object and it's overlapping the final merged mesh you just created, causing the problem.